Solve for $x$ : $2x^2 + 10x + 8 = 0$
Dividing both sides by $2$ gives: $ x^2 + {5}x + {4} = 0 $ The coefficient on the $x$ term is $5$ and the constant term is $4$ , so we need to find two numbers that add up to $5$ and multiply to $4$ The two numbers $1$ and $4$ satisfy both conditions: $ {1} + {4} = {5} $ $ {1} \times {4} = {4} $ $(x + {1}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 1) (x + 4) = 0$ $x + 1 = 0$ or $x + 4 = 0$ Thus, $x = -1$ and $x = -4$ are the solutions.